Tegmark's Mathematical Universe

Dear Florin,

thanks for replying.

My gut feeling is, that your approach is thought-out very well and i haven't any doubts that it is also the case with your mentioned and used mathematical tools, like orthogonal groups SO(p,q), elliptic, parabolic, and hyperbolic classes etc. It seems to fit all well together and if one can indeed succeed by singling out certain exclusively unique mathematics for our universe, this would be a great result and of deep philosophical importance. I cannot comment on any of the mathematical tools because i am not an expert in this area, but i don't doubt in any way that you have the deep understanding of these tools to draw the right conclusions out of them.

My only doubt was, that for eliminating an ontology of ultimate reality one had to presuppose that physical reality is indeed "only" a universal turing machine. If the latter would be true, i am not sure if this would mean that an exclusively mathematical procedure can indeed prove the exclusiveness of mathematics. I understand your approach in this way, that if one could obtain indeed physics axiomatization, then this result could serve as a strong indicator that an exclusively mathematical procedure can prove it's own exclusiveness by comparing it to the timless content of the platonic realm and at the same time prove the exclusiveness of this platonic realm of mathematics - by comparing it with the maths of our physical world.

I understood your example with the different PCs, emulating different worlds/ontologies, as an example of the impossibility to fix a certain ontology onto our *physical* universe,if it would be indeed "only" a universal turing machine. The precondition for the physical world to be a universal turing machine is, that the physical universe and the laws within are consistent, coherent and universally true (that's a necessity, but not sufficient). But does your Gedankenexperiment also apply to the *Gödel-restricted* realms of mathematical, infinite landscapes/systems/frameworks? Means, to deduce out of the concept of a universal turing machine that the platonic realm of maths doesn't need an ontology? Or have i to understand it in that way, that every platonic consistent system/framework/part can be understood as a turing machine within its own area?

Eugen - nice to met you again here. Very interesting discussion here, as always on fqxi! Wish you all the best for the contest results!

Dear Florin,

You state, "I do not know about consciousness, but I do know about free will" "Free will is equivalent to the ability to decide what to measure in QM... there is a 'free will theorem' in QM"

I would not say 'equivalent', but the sense of your statement is correct. Without getting too far into semantics, I question whether one can 'not know' awareness and 'know' free will. They are, I believe, inseparably intertwined. If as you state elsewhere, you believe that "consciousness is an emergent property" then it is Darwinian, and two things follow: Awareness would have no survival advantage without free will (the ability to act on this awareness) and free will is meaningless without awareness. By this I mean that 'having a math model or theorem for 'free will' is not what I mean by 'know'. Know is for me personal experience; it is the territory of reality. Math and theorems are maps.

In reply to Stefan, you state that "consciousness is an emergent property". This is your belief, and it is the consensus belief, but Climate-gate has recently focused attention on the fact that science is not consensus. It was the consensus belief in the middle ages that "flies emerged from rotten meat". I believe that 'emergent consciousness' is similarly mistaken.

The fact is that no one, anywhere, has developed a model or explanation for how conscious awareness and volition can arise from 'stupid' material. I have written a number of chapters on this -- far too much to go into here. But recall that I define intelligence as 'consciousness plus logic', i.e., the evolution (emergence) of logical hardware is required for intelligence to develop. Intelligence is required to create calculus, even to develop ideas of past and future (based on recall and projection of information stored in the logical machinery).

I am not trying to convert you from your beliefs -- only about twenty percent of the FQXi authors appear to take consciousness seriously as something that physics must deal with. But your statement "consciousness is an emergent property" is so strong and unqualified, I felt the need to throw in a little qualification.

You do state that your gut feeling is that it is not relevant to physics. Depends. At the particle physics level you are absolutely correct. Although I show (Chromodynamics War) how the C-field can explain particle families, provide an intuitive understanding of the mechanism of the weak force, and also provide the quark confinement associated with the strong force, I do not believe that awareness or free will have any significant part to play here.

I do suspect that awareness comes into play in entanglement, and I believe consciousness provides the biophysics explanation for the first living cell, which otherwise is infinitely unlikely to ever occur.

But it is cosmology where consciousness may come into its own. As I show in my essay, the C-field provides an inflation mechanism that is more 'real' than any of the imagined fields currently proposed. Not only is this a 'dark energy' source but the energy of the C-field also offers a dark matter explanation. And the C-field, as I explain in 'Gene Man's World' provides an explanation for Zwicky's 'flat rotation curves' so that a messy MOND is not needed.

Klingman post continued:

Continuation of Klingman post:

But I'd like to address your question, "why is our universe happening only once? ... Earth is not the center of the solar system, our sun is not the center of our galaxy, etc. etc." You may be unaware that the WMAP measurements, circa 2003?, in analyzing various polar distributions, quadrupole, octupole, etc, expected to find uncorrelated directions for each pole. They were amazed to find one axis that appears to be correlated with the solar system to 99.996 percent. One of the FQXi members, Glen Starkman, wrote a fascinating article in Scientific American in 2005 about this axis.

And to quote Wiaux, "The correct explanation of these unexpected correlations of the low-l features of the microwave background with each other and with the solar system is currently not known."

Why haven't you heard of this? For obvious reasons, physicists are embarrassed to talk about solar system-centric phenomena. There was a three year period of silence, but recently Science has quoted cosmologists, "It's there, everyone agrees." With their superb wit, the cosmologists have named it "the axis of evil". And they ask, "Is it significant?"

How could an unexpected solar-centric axis of the universe be significant?

And how could the Pioneer orbits, that appear to show a 'flat rotation curve' behavior in the vicinity of the Earth that is six times greater than that seen in other galaxies and galactic clusters, be significant?

Florin, In July 2008, A Physical Review Letters paper by Clarkson, Bassett and Lu, "A General Test of the Copernican Principle" addressed the problem obliquely by saying, "It is ever more clear that this matter must be settled observationally without theoretical bias." (One might even say theological bias, as it is quite clear that the 'multiverse' was created for theological reasons, as an alternative explanation for fine tuning.)

Now if one were to ascribe these unexpected and unexplained phenomena to the consciousness field, then there appear to be two possibilities: Either the Earth is, by pure chance, located on the axis of the 'major C-field vortex of the universe' and is thereby preferentially positioned for life to emerge, or the emergence of life on Earth has so strengthened the local C-field that its inflationary aspect has effectively imprinted on the CMB.

Florin, the point is that the C-field at least qualitatively makes sense of unexplained mysteries at the particle level, the atomic physics level, the biophysics level, the human level, and the level of the universe.

As Planck stated, "theories are never abandoned until their proponents are all dead. Science advances funeral by funeral."

Nothing has changed since Planck, except that there are perhaps a thousand times as many proponents. That is why the failure to find the Higgs is so important. Perhaps the last, best chance to get physics back on the right track! If physicists ignore the significance of new discoveries and keep on the old path, I predict a long, frustrating, dry spell for physics. Because the C-field qualitatively and in some cases quantitatively explains these phenomena, I predict no Higgs, no SUSY, no axions, no WIMPs, no right-handed neutrinos, no new particles. They are not needed if the C-field is real (as Tajmar and others seem to experimentally prove). If the failure of these to show at LHC doesn't wake physicists up, we're lost.

The odds that the physics community, embedded up to their ears in a scientific establishment that does not like major change, is most unlikely to look in new directions. We'll just 'tweak here, tweak there' and go on publishing and writing grants. As the UC Berkeley philosopher was advised, "It's OK to work on consciousness, but get tenure first."

That is what makes the FQXi contests so praiseworthy. It is perhaps the only serious physics community, with serious scientists as members, that is open to publishing new ideas, and for that it deserves high praise indeed.

Edwin Eugene Klingman

I wrote more on nonassociativity in physics on the site involving warp drives. This is in keeping with trying to illustrate something about how nonassociative principles might operate in physics. If you (Ray, Florin etc) are interested you could reply here. I am not entirely pleased with the intellectual level of discussion on the warp drive site, or frankly most of the blog sites.

LC

Dear All,

I checked out the warp drive thread enough to find Ray Munroe's statement:

"Could we control tachyons inside a gravitational bottle? It would be the gravitational equivalent of using a magnetic bottle (such as a tokamak) to confine plasma. If we could contain tachyons thus, we may be able to release them such that we can steer our spaceship. Could we envelope our spaceship with a tachyonic field and trick Gravity into thinking that the entire spaceship is a tachyon? And could we steer such a spaceship?"

I've noted on his thread that this 'gravitaional bottle' forms an explanation for the confinement of quarks, currently attributed to 'the strong force'. It also provides a mechanism for sustaining the 'cigar shape' of deuterium, whereas QCD would predict a six quark 'collapse' to some spherical combination. And it also can explain the negative 'core' of the neutron, whereas all QCD predictions call for a positive core. All of this follows from viewing the C-field as the rotational aspect of the G-field.

Hopping around the threads and essays certainly proves that there is no end of 'wild' speculation. For this reason it seems more important than ever to PREDICT things. To my knowledge there is no place where one may go to find various predictions for the LHC.

I would invite those who make predictions to place them here. It would be nice to see just what is predicted for LHC (or WMAP-follow-ons, etc.) before the results are known and explained 'post-dictively'.

If one can't predict anything, what exactly is the point of intellectual analysis. Is it to see who can describe the universe best by looking in a rear-view mirror?

If predictions still mean anything in physics, let's hear some.

Sincerely,

Edwin Eugene Klingman

Dear Ed,

I will reply in turn to each message. Let's start with:

"As for Newton's equation and instantaneous change, why would not the same logic apply to Coulomb's equation, since they are formally equivalent."

Indeed, but the E and B fields are linked by Maxwell's equations, and a change in one induces a change in the other and vice-versa. In your equations C depends on G, but G does not depend on C and this is the problem. G depends only on the mass distribution and when that changes G changes everywhere with it instantaneously.

Regards,

Florin

Florin,

Thanks... But changes in the G-field are linked to the C-field, thereby extracting energy from G. Why is this insignificant?

Ed

Dear Stefan,

You state: "My only doubt was, that for eliminating an ontology of ultimate reality one had to presuppose that physical reality is indeed "only" a universal turing machine."

This is not what I was saying. A universal Turing machine (UTM) violates the third reality principle: "infinite complexity" because the algorithmic information content is limited by the program running on the UTM.

"Or have i to understand it in that way, that every platonic consistent system/framework/part can be understood as a turing machine within its own area?"

Something along those lines, but a bit more general. The platonic world of math is a collection of axiomatic systems. Each axiomatic system exists on its own. In math there are many types of logics which go beyond an UTM ability.

The UTM usage in my argument should be understood in two ways. First, we fully understand the UTM theory and we have a rigorous framework of discussion free of conflicting interpretations. That is, the usage of the UTM adds clarity. Second, different ontologies do not have to be like our own universe's ontology. In other words, there is an ontological democracy. And indeed, some ontologies are much more interesting and richer in content than other ontologies, but there is no objective value that can be attached to one ontology vs. another. To be able to make judgments about various ontologies, is to have a meta framework in place, and this simply does not exists. The only thing we can use is infinite complexity vs. finite complexity.

Dear Ed,

Please understand that my ideas are still evolving. My models definitely have a five-fold 'pentality' symmetry that is relevant to the golden ratio (file attached). The fifth vertex corresponds to 'scalar fermions'. These scalar fermions can be chromo-tachyons that obey the strong force, or lepto-tachyons that obey the Electro-Weak forces. They might even be related to the Higgs (research in progress). I don't have a gravitational bottle - it sounds like a worm hole or black hole. I haven't studied the interactions of gravity and consciousness closely. My model also has a triality symmetry. Like Lisi, I think the triality symmetry has to do with three generations. However, there is a possible color triality as well. In my models, the apparent three-fold color triality becomes a four-fold color quartality of (red, green, blue, white). H4 has a four-fold quartality symmetry, and E8 has an eight-fold octality (4x2?) symmetry. Lawrence Crowell also has a triality symmetry.

I agree that it is relevant to state our predictions prior to the LHC's results, however a robust enough idea can be adjusted to fit the data. I am still trying to understand these weird scalar fermions.

Have Fun!

RayAttachment #1: 1_goldenratio.pdf

Dear Ed,

>"free will is meaningless without awareness"

I disagree. Even a frog has free will, but it does not have awareness.

>"'emergent consciousness' is similarly mistaken".

Not that I am an expert, but can we explain consciousness in reductionism fashion? When a piece of the brain dies, the other parts can take over and consciousness looks to me to have a "holographic" property. The brain function resembles the best a spin glass, and awareness looks something that is much more than the sum of its parts. In this way I meant it as emergent.

>"I define intelligence as 'consciousness plus logic', i.e., the evolution (emergence) of logical hardware is required for intelligence to develop. Intelligence is required to create calculus, even to develop ideas of past and future (based on recall and projection of information stored in the logical machinery)."

Intelligence (or smartness) looks to me as the ability to create information (reduce entropy) in a given environment. To invent calculus, you need something more: creativity. By algorithmic information theory, it is impossible to create the new axioms required by a new mathematical area, e.g. calculus. What you do to beat this theorem is to take fragments from different axiomatic systems, and try to extrapolate and see what is consistent in a survival of the fittest approach. Creativity is therefore requiring being able to make connections between separate independent areas.

>"I do suspect that awareness comes into play in entanglement, and I believe consciousness provides the biophysics explanation for the first living cell, which otherwise is infinitely unlikely to ever occur."

I do not know how to precisely define awareness, but entanglement is well understood and refers to basically a composite system and the fact that one subsystem is correlated with the other. A naïve idea would be a left and a right glove. One person has one in a box, while another person has the other one in another box. When observer A opens his box and finds the right glove, he knows that when observer B opens his box it will be the left glove. But this is naïve because in QM in addition to this, entanglement means that there is no factorization possible between the two subsystems. The root cause is that the size of the Hilbert space of the composite system is larger than the product of the sizes of the subsystem's Hilbert spaces. The extra degrees of freedom arising out of adding amplitudes and not probabilities is responsible for the lack of factorization and the weirdness of QM.

>"But I'd like to address your question, "why is our universe happening only once? ... Earth is not the center of the solar system, our sun is not the center of our galaxy, etc. etc." You may be unaware that the WMAP measurements, circa 2003?, in analyzing various polar distributions, quadrupole, octupole, etc, expected to find uncorrelated directions for each pole. They were amazed to find one axis that appears to be correlated with the solar system to 99.996 percent. One of the FQXi members, Glen Starkman, wrote a fascinating article in Scientific American in 2005 about this axis."

I was just not aware of this, I will look into it.

>"And how could the Pioneer orbits, that appear to show a 'flat rotation curve' behavior in the vicinity of the Earth that is six times greater than that seen in other galaxies and galactic clusters, be significant?"

I am not an expert in the Pioneer anomaly, so I cannot comment.

>"The odds that the physics community, embedded up to their ears in a scientific establishment that does not like major change, is most unlikely to look in new directions."

"That is what makes the FQXi contests so praiseworthy. It is perhaps the only serious physics community, with serious scientists as members, that is open to publishing new ideas, and for that it deserves high praise indeed."

This is correct. And FQXi does fill a very big gap in this respect.

Regards,

Florin

Dear Lawrence,

I read your post, but I am still having difficulty to make the connection with the S matrix. On the other hand, I have an idea of how to obtain supersymmetry from quantions, it will take me quite some time to finalize it (I hope my intuition is right and it will work out until the very end).

I finished the 12 GR lectures and now I am seeing all the other Susskind's classes. The mystery of his approach is solved: he lectures continuous education classes with no final exam. Those classes would have been good as preparation for a qualifier: you can just listen to them without taking notes and getting insight into things which escaped notice the first time when you are busy absorbing the new material.

Ray,

"Like Lisi, I think the triality symmetry has to do with three generations."

Is this right? Is not triality related to the interaction vertex in Feynman diagrams: one fermion line emits a boson line, and continues as a fermion line? Equivalently, this has to do with the gauge symmetry (for example the A_mu in electromagnetism acts as a connection). But the gauge symmetry of the standard model is independent of the generations and therefore triality should have nothing to do with it.

Dear Edwin,

sorry for having confused your first/second name in my last post, i was just too deep absorbed in my lines of reasoning... By the way - interesting issue, the wmap measurement and the correlation of the axis to our solar system. I have to read more about it.

Dear Florin,

thanks for your clarifications. Yes, i wondered, if our physical universe would be indeed only a UTM, how could one then ever reach out of this area to the platonic realms of maths? To reach out to new information, one has to consider that at least our ontology/universe isn't a "closed system" in the sense of finite information content. In that way i understand infinite complexity in your approach as ingredient for creativity, free will and consciousness.

As you can imagine, my own approach differs from yours when it comes to the nature of the essence beyond time and space. For me the essence isn't maths, but awareness/consciousness. But not in a human sense of self-awareness. From outside of this awareness, for observers like us, it looks like consciousness could serve as the ultimate ontology, but the question that follows out of this intendation is automatically "What is the cause/root of that awareness?".

From inside of it this question doesn't make sense, because this awareness/source of ultimate reality is simultaneously the source of all opposites - and therefore the source of all questions and answers. By the very first differentiation of that awareness - by exploring the idea of conscious/unconscious for the purpose of some interior intentions, it created the question about identity/difference and the following self-similar differentiation process generates the answer to this idea/question.

This process may be infinite. It may generate infinitely many sub-conscious entities that have to transcend the initial idea of self/not-self to come back to the inital awareness with a richer knowledge of its ontology - in the meaning of quality of experience. This experiences heighten the complete initial awareness. Though this initial awareness doesn't need an explanation of its own ontology, because it's essential awareness is self-evident in each instant of it, it needs to explore its own quantitative meaning and its possible borders to enrich its quality of experience. In this sense, experience is the only "ontology" and it is subjective/interior.

Max Tegmark has mapped the octopole CMB on a sphere and it looks quite beautifull here.

There I am happy dear Mr Tegmark ,yes the universe is a sphere in evolution .

But I don't see my name, it is not serious ,I have the habit .

You are going to have the nobel price dear Mr Tegmark and his team .

Congratulations for this splendid disovery ,the universe is a sphere .

PS Mr Tegmark ,you have forgoten the universal center where all turns around .An other poit is the variability of the volume of this universal sphere .A specific dynamic exists since the begining .Expension and contraction .

Regards

Steve

Serious error ,the center ......

Dear Florin,

I suspect that in Lawrence's full blown 26-D model, that one octonion is the initial fermion, one octonion (and the global G2 triality operator) is the interaction boson, and the third octonion is the final fermion. This may be related to Mohammed Sanduk's 'Three Gear Model' essay.

But at some level of decomposition, I expect the generational structure to 'make sense'. I am convinced that if there are 3, 4, 5, or etc. generations, then there must be a symmetry that enforces that reality. There seem to be two triality symmetries in Lawrence's 26-D model: one buried within E8 (240 roots = 8x(2x3x5)), and one connected to the global G2 (12 roots = 2x(2x3)). Thus, we could have a generational triality and an interaction vertex triality.

Dear Steve,

Tegmark's map is impressive, but he has non-spherical results mapped on a spherical map. Is that really spherical in evolution? My truncated icosahedon (soccer ball) is more spherical.

Have Fun!

Ray

The space of the universe is probably R^3, or Euclidean space which extends indefinately. THe CMB represents a radial distance out, and as observed with photons also a time in the past, when the universe ceased to be radiation dominated and became matter dominated. The CMB is then a region of a past spatial surface, with geometry or topology R^3, which intersects our past light cone.

Cheers LC

A flat spatial surface (flat on average) is one where the holographic principle works with the Bekenstein bound. There is a bit of background here that I don't want to get into for brevity's sake. The universe still is expanding, as points on a spatial 3-surface keep sliding apart, where any frame at any given point will see distant points slide away at velocities which "approach infinity." Already we observe galaxies with z > 1, which means these are frame dragged galaxies on a comoving frame which has velocity > c. However, there is a cosmological horizon present which precludes any idea of FTL transport on a closed path --- to somewhere and back for instance. Similarly, any particle which passes the event horizon of a black hole is moving faster than light relative to a distant observer.

Cheers LC